Backlog-based wireless access schemes are simple and inherently distributed, yet provide a striking capability to match the optimal throughput performance of centralized scheduling mechanisms in a wide range of scenarios. Unfortunately, the type of activation rules for which throughput optimality has been established, may result in excessive backlogs and delays. The use of more aggressive/persistent access schemes than these can improve the delay performance, but does not offer any universal maximum-stability guarantees. Motivated by the above issues, we use fluid limits to explore the (in)stability properties of backlog-based random-access algorithms. Such fluid limits have varying qualitative properties, dependent on the specific scenario, ranging from ones with smooth deterministic features, to others which exhibit random oscillatory characteristics. It turns out that more aggressive access schemes continue to provide maximum stability in some networks, e.g. complete interference graphs. As we show however, in other topologies such schemes can drive the system into inefficient states and thus cause instability. Simulation experiments are conducted to illustrate and validate the analytical results.